A particle free to move along the x -axis has potential energy given by U ( x ) = k [1 –…
Physics · JEE Advanced · NTA Exams — Oscillations and Waves
A particle free to move along the x-axis has potential energy given by U(x) = k [1 – exp(–x2)] for –∞ ≤ x ≤ +∞, where k is a positive constant of appropriate dimensions. Then
- at points away from the origin, the particle is in unstable equilibrium
- for any finite nonzero value of x, there is a force directed away from the origin
- if its total mechanical energy is k/2, it has its minimum kinetic energy at the origin.
- for small displacements from x = 0, the motion is simple harmonic.
Answer
(D) for small displacements from x = 0, the motion is simple harmonic.
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